C being constant in all frames deduced backwards

Sorry, this is a really basic question which will possibly annoy you and I'm embarrassed to even be asking this

But if you travel at say 0.5c to the left (relative to your axes) and a photon of light goes past you to the right at c (again relative to your axes) what are the sums that you do to measure its speed and get c?

Obviously the old way of approaching it is to say "Oh, its 0.5c - c = -0.5c relative to my motion" but we know that it's not.

So how do we actually apply the lorentz transformation to get the result c? I can't find anything going over this so basically